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Math Help - Tangent line and Perpendicular

  1. #1
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    Tangent line and Perpendicular

    Hello

    Determine the coordinates of the point on the graph f(x) = (2x+1)^0.5 where the tangent line is perpendicular to the line 3x +y +4 = 0

    ----------------------------------
    This is what I did so far
    f'(x) = 0.5 (2x+1) ^-0.5 (2)
    = 1 / (2x+1) ^0.5

    Not sure what to do after
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  2. #2
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    Quote Originally Posted by jamson254 View Post
    Hello

    Determine the coordinates of the point on the graph f(x) = (2x+1)^0.5 where the tangent line is perpendicular to the line 3x +y +4 = 0

    ----------------------------------
    This is what I did so far
    f'(x) = 0.5 (2x+1) ^-0.5 (2)
    = 1 / (2x+1) ^0.5

    Not sure what to do after
    find the slope of the line, m ... the perpendicular slope is -1/m

    set f'(x) = -1/m , then solve for x ... finally, evaluate the y-coordinate from f(x).
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  3. #3
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    Thanks is this correct?
    3x+y+4=0
    Y = -3x-4

    Slope = -3

    Perpendicular slope = 1/3

    Let F' = 1/3

    1/3 = 1/ (2x+1)^0.5



    3 = (2x+1) ^.5
    squaring both sides
    9 = 2x+1
    x = 4

    F(4) = 3

    Point is (4,3)
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  4. #4
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    correct
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  5. #5
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    Thanks a lot for helping me
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